Upper bounds on the Kolmogorov distance (and, equivalently in this case, on the total variation distance) between the Student distribution with degrees of freedom () and the standard normal distribution are obtained. These bounds are in a certain sense best possible, and the corresponding relative errors are small even for moderate values of . The same bounds hold on the closeness between and with . Comparisons with known bounds are made.
DOI : 10.1051/ps/2014014
Mots-clés : Student’s distribution, standard normal distribution, Kolmogorov distance, total variation distance, probability inequalities
@article{PS_2015__19__24_0, author = {Pinelis, Iosif}, title = {Exact bounds on the closeness between the {Student} and standard normal distributions}, journal = {ESAIM: Probability and Statistics}, pages = {24--27}, publisher = {EDP-Sciences}, volume = {19}, year = {2015}, doi = {10.1051/ps/2014014}, mrnumber = {3374867}, zbl = {1332.62054}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/ps/2014014/} }
TY - JOUR AU - Pinelis, Iosif TI - Exact bounds on the closeness between the Student and standard normal distributions JO - ESAIM: Probability and Statistics PY - 2015 SP - 24 EP - 27 VL - 19 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ps/2014014/ DO - 10.1051/ps/2014014 LA - en ID - PS_2015__19__24_0 ER -
%0 Journal Article %A Pinelis, Iosif %T Exact bounds on the closeness between the Student and standard normal distributions %J ESAIM: Probability and Statistics %D 2015 %P 24-27 %V 19 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ps/2014014/ %R 10.1051/ps/2014014 %G en %F PS_2015__19__24_0
Pinelis, Iosif. Exact bounds on the closeness between the Student and standard normal distributions. ESAIM: Probability and Statistics, Tome 19 (2015), pp. 24-27. doi : 10.1051/ps/2014014. http://archive.numdam.org/articles/10.1051/ps/2014014/
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